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### The Maxima on-line user's manual

Algebra Calculator

#### Trigexpand

Function: trigexpand (<expr>) Expands trigonometric and hyperbolic functions of sums of angles and of multiple angles occurring in <expr>. For best results, <expr> should be expanded. To enhance user control of simplification, this function expands only one level at a time, expanding sums of angles or multiple angles. To obtain full expansion into sines and cosines immediately, set the switch `trigexpand: true`.

`trigexpand` is governed by the following global flags:

`trigexpand` If `true` causes expansion of all expressions containing sins and coss occurring subsequently.

`halfangles` If `true` causes half-angles to be simplified away.

`trigexpandplus` Controls the "sum" rule for `trigexpand`, expansion of sums (e.g. `sin(x + y)`) will take place only if `trigexpandplus` is `true`.

`trigexpandtimes` Controls the "product" rule for `trigexpand`, expansion of products (e.g. `sin(2 x)`) will take place only if `trigexpandtimes` is `true`.

Examples:

```          (%i1) x+sin(3*x)/sin(x),trigexpand=true,expand;
2           2
(%o1)               - sin (x) + 3 cos (x) + x
(%i2) trigexpand(sin(10*x+y));
(%o2)          cos(10 x) sin(y) + sin(10 x) cos(y)```

There are also some inexact matches for `trigexpand`. Try `?? trigexpand` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

trigexpand(x+y);

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f: (sin*(x+y));

trigexpand(f);

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##### trigexpand

trigexpand(expand((x^...

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##### trigexpand

p: trigexpand(sin*(x ...

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##### trigexpand

f : ((x+3)*(x-3)-((x+...

trigexpand(f);

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%e^(%i*w);

trigexpand;

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##### trigexpand

trigexpand((3*x+5)^2-...

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##### trigexpand-trigsimp

sin2x=trigexpand(sin(...

sin3x=trigexpand(sin(...

cos3x=trigexpand(cos(...

Calculate

p:(sin*(x+y));

trigexpand (p);

Calculate

##### trigexpand

trigexpand (2*(sin*x)...

Calculate